Final answer:
The z-score for an 89% confidence interval is not standard, but it would be slightly less than the z-score for a 90% confidence interval, which is 1.645.
Step-by-step explanation:
The z-score that corresponds to a 89% confidence interval is not typically found in standard z-tables because it is not a common value used in statistics. However, for an approximate value, we can look at related information. A 90% confidence interval typically uses a z-score of approximately 1.645, which is the critical value that leaves 5% in each tail of the normal distribution.
To find the exact z-score for an 89% confidence interval, one would utilize statistical software or a z-table that provides more precise values. However, one can infer that because an 89% confidence interval is slightly less than a 90% confidence interval, the z-score would be slightly less than 1.645. This is because as we decrease the confidence level, the corresponding z-score that captures the central portion of the normal distribution also decreases.
The z-score that corresponds to an 89% confidence interval can be found by subtracting the confidence level from 1 and then dividing the result by 2. In this case, the calculation would be (1 - 0.89) / 2 = 0.055. Using a z-table, we can find that the z-score for an area of 0.055 to the left is approximately -1.65.